Algebraic Graph Theory Seminar - Chris Godsil

Title: Cospectral graphs, cospectral complements

Abstract:

It is an important open question whether ‘most’ graphs are
determined by their spectrum. Somewhat surprisingly, the computational
evidence is that graphs that are cospectral tend to have cospectral
complements. This is a surprise because, in general, there is no simple
relation between the spectrum of the graph and that of its complement.
But there are relations, and my talk will present some of what we
know about them.